Problem: Michael is 6 years older than Vanessa. Seven years ago, Michael was 3 times as old as Vanessa. How old is Vanessa now?
Solution: We can use the given information to write down two equations that describe the ages of Michael and Vanessa. Let Michael's current age be $m$ and Vanessa's current age be $v$ The information in the first sentence can be expressed in the following equation: $m = v + 6$ Seven years ago, Michael was $m - 7$ years old, and Vanessa was $v - 7$ years old. The information in the second sentence can be expressed in the following equation: $m - 7 = 3(v - 7)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $v$ , it might be easiest to use our first equation for $m$ and substitute it into our second equation. Our first equation is: $m = v + 6$ . Substituting this into our second equation, we get the equation: $(v + 6)$ $-$ $7 = 3(v - 7)$ which combines the information about $v$ from both of our original equations. Simplifying both sides of this equation, we get: $v - 1 = 3 v - 21$ Solving for $v$ , we get: $2 v = 20$ $v = 10$.